A chemical vapor infiltration method for densifying porous substrates disposed in ring-shaped stacks is known from WO 96/33295. In order to achieve dwell times of the vapor phase which are as short as possible, the vapor phase is introduced on the inlet side of the reaction zone into the central interior space of the stack of ring-shaped disks, and is discharged on the outlet side of the reaction zone from the outer circumferential space surrounding the stack on the outside. The outer circumferential space is closed toward the inlet side, and the central interior space is closed toward the outlet side. Thereby, the transverse slots formed between the disks inevitably join the flow path between the inlet and the outlet of the reaction zone. The infiltration is carried out at a temperature of typically 1,000° C. and at a low pressure of typically 1 kPa. However, this known method cannot be used in methods of the type according to the invention, where substantially higher pressures are applied, due to a significant vapor phase nucleation, such as soot production in case of carbon infiltration.